Hückel Theory and Optical Activity
Prof. Bart Kahr
Department of Chemistry, New York University, NY
Hückel theory is an approximate molecular orbital theory for planar, conjugated hydrocarbons whereas optical activity is typically associated with molecular chirality, a geometrical property of three-dimensional structures. Hückel theory and optical activity are subjects that at first blush brook no intersection. Why the conjunction “and” in the title? Some achiral compounds can indeed be optically active, but these have been traditionally excluded from considerations of optical activity because the spatial average of the optical activity of such compounds is zero. Thus, nothing can be measured in solution. On the other hand, these are perfectly appropriate targets for measurement on crystals. Optical rotations and rotatory strengths are here calculated for planar, conjugated hydrocarbons with the aim of determining to what extent the sum-over-π→π* rotatory strengths are sufficient to account for non-resonant optical activity, as well as to what extent qualitative molecular orbital theory can be used to interpret chiroptical structure-property relations. It is shown that by restricting our analyses to planar π-systems, an intuitive understanding of the vexing property of optical activity is forthcoming for the following reasons: Wave functions under the Hückel approximations are simply determined and graphically computed to yield transition dipole and quadrupole moments; the forms of the gyration tensors are given by symmetry with simple representation surfaces whose orientations are completely (C2v) or partly (Cs) determined by symmetry; transition electric dipole and magnetic dipole moments have fixed, orthogonal dispositions relative to one another, and the most optically active directions are found at their bisectors. Throughout, the emphasis is on reckoning long wavelength optical rotation using simple models that are part of organic chemistry pedagogy. Attempts to measure the optical activity of oriented, isolated achiral molecules is also discussed.
